The Mass, Normalization and Late Time behavior of the Tachyon Field

TL;DR

This paper investigates the dynamics and properties of the tachyon field, including its mass, transformation to a canonical form, and late-time behavior, with implications for dark energy models.

Contribution

It introduces a new method to determine the tachyon mass, derives a transformation to a canonical scalar field valid for large velocities, and analyzes the late-time behavior of the tachyon.

Findings

Tachyon mass is identified as the pole of the propagator, differing from standard literature.

The transformation to a canonical scalar field is valid for both small and large velocities.

The normalized tachyon field is constrained within the zeros of its potential.

Abstract

We study the dynamics of the tachyon field $T$. We derive the mass of the tachyon as the pole of the propagator which does not coincide with the standard mass given in the literature in terms of the second derivative of $V(T)$ or $Log[V(T)]$. We determine the transformation of the tachyon in order to have a canonical scalar field $\phi$. This transformation reduces to the one obtained for small $\dot T$ but it is also valid for large values of $\dot T$. This is specially interesting for the study of dark energy where $\dot T\simeq 1$. We also show that the normalized tachyon field $\phi$ is constrained to the interval $T_2\leq T \leq T_1$ where $T_1,T_2$ are zeros of the original potential $V(T)$. This results shows that the field $\phi$ does not know of the unboundedness of $V(T)$, as suggested for bosonic open string tachyons. Finally we study the late time behavior of tachyon field using the L'H\^{o}pital rule.